The Planck results, combined with BAO measurements, show that our
Universe is almost spatially flat with a spectrum of nearly scale
invariant adiabatic fluctuations. In addition, the Planck data show
no evidence for primordial non-Gaussianity [1]}, [2]}. These results are consistent with single field
models of inflation (see [3]}, [4]}, [5]} and references
therein). If the Universe did indeed experience an inflationary phase,
there should exist a nearly scale-invariant spectrum of tensor
fluctuations [6]} with a highly uncertain
amplitude that depends on the energy scale of inflation. Allowing
tensor modes is therefore one of the best motivated extensions of the
base \(\rm {\Lambda CDM}\)  model and their detection would provide an important clue
towards understanding the physics of inflation. The
Planck temperature spectra provide relatively poor constraints on
tensor modes because of cosmic variance on large scales
[7]}. However, tensor modes can be detected via B-mode
polarization anisotropies [8]}, [9]}. At
present, the strongest constraints on primordial B-mode anistropies
come from the BICEP2-Keck Array collaboration [10]}, [11]}, [12]}, developing on earlier work by the BICEP2
collaboration [13]}. Joint constraints using our
CamSpec likelihoods combined with the BICEP2-Keck Array measurements
of [12]} (denoted BK15) are plotted in
Fig.  REFAs in PCP13-PCP18, we report
constraints on the tensor-scalar ratio \(r_{0.002}\) , which is the
relative amplitude of the tensor and scalar primordial fluctuation
spectra at a pivot scale of \(k = 0.002 \ {\rm Mpc}^{-1}\) . The tensor
spectral index is set to the value expected in single-field inflation
models, \(n_t = -r_{0.05}/8\) , where \(r_{0.05}\)  is the
tensor-to-scalar ratio at a pivot scale \(k = 0.05 \ {\rm Mpc}^{-1}\) . The scalar spectral index \(n_s\)  is defined at a pivot
scale of \(k = 0.05 \ {\rm Mpc}^{-1}\)  (see Eq. 2 of
PCP18)..
The 95% upper limits on the tensor-scalar ratio given by the 12.5HMcl
TTTEEE+BK15+BAO+lensing likelihood are
\(r_{0.002} < 0.058, \qquad r_{0.05} < 0.062, \) 
